Structural changes in nonlocal denoising models arising through bi-level parameter learning

DOI10.1007/s00245-023-09982-4OpenAlexW4362733265MaRDI QIDQ2701086

Hidde Schönberger, Rita Ferreira, Elisa Davoli, Carolin Kreisbeck

Publication date: 27 April 2023

Published in: Applied Mathematics and Optimization (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2209.06256

zbMATH Keywords

\(\Gamma\)-convergenceparameter optimizationbi-level learning schemeimage denoising modelsnonlocal regularizers

Mathematics Subject Classification ID

Methods involving semicontinuity and convergence; relaxation (49J45) Existence theories for optimal control problems involving relations other than differential equations (49J21)

Related Items (1)

A sufficient condition for the lower semicontinuity of nonlocal supremal functionals in the vectorial case

Cites Work

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• Nonlinear total variation based noise removal algorithms
• Fractional elliptic equations, Caccioppoli estimates and regularity
• Weak lower semicontinuity and relaxation for a class of non-local functionals
• Hitchhiker's guide to the fractional Sobolev spaces
• A new approach to Sobolev spaces and connections to \(\Gamma\)-convergence
• Bilevel parameter learning for higher-order total variation regularisation models
• The structure of optimal parameters for image restoration problems
• Characterisation of the weak lower semicontinuity for a type of nonlocal integral functional: the \(n\)-dimensional scalar case
• Some relaxation problems in optimal control theory
• Gamma-convergence and optimal control problems
• Completion by gamma-convergence for optimal control problems
• An introduction to \(\Gamma\)-convergence
• Parametrized measures and variational principles
• Image recovery via total variation minimization and related problems
• On an open question about functions of bounded variation.
• Non-local functionals related to the total variation and connections with image processing
• Optimal selection of the regularization function in a weighted total variation model. I: Modelling and theory
• One dimensional fractional order TGV: gamma-convergence and bilevel training scheme
• Bilevel parameter learning for nonlocal image denoising models
• Cartesian convexity as the key notion in the variational existence theory for nonlocal supremal functionals
• Learning nonlocal regularization operators
• Lower semicontinuity and relaxation of nonlocal \(L^\infty\)-functionals
• Bilevel optimization. Advances and next challenges
• Spectral approximation of fractional PDEs in image processing and phase field modeling
• A PDE approach to fractional diffusion in general domains: a priori error analysis
• Image denoising: learning the noise model via nonsmooth PDE-constrained optimization
• Adaptive image processing: first order PDE constraint regularizers and a bilevel training scheme
• Non-Local Functionals for Imaging
• Global Solutions of Variational Models with Convex Regularization
• Nonlocal Operators with Applications to Image Processing
• Can the Nonlocal Characterization of Sobolev Spaces by Bourgain et al. Be Useful for Solving Variational Problems?
• Insights Into Analysis Operator Learning: From Patch-Based Sparse Models to Higher Order MRFs
• Lower Semicontinuity and Relaxation Via Young Measures for Nonlocal Variational Problems and Applications to Peridynamics
• A bilevel approach for parameter learning in inverse problems
• Bilevel optimization, deep learning and fractional Laplacian regularization with applications in tomography
• Bilevel Training Schemes in Imaging for Total Variation--Type Functionals with Convex Integrands
• Modern regularization methods for inverse problems
• Sobolev Spaces with Non-Muckenhoupt Weights, Fractional Elliptic Operators, and Applications
• Learning optimal spatially-dependent regularization parameters in total variation image denoising
• Existence for Nonlocal Variational Problems in Peridynamics
• Γ-convergence and absolute minimizers for supremal functionals
• Total Generalized Variation
• Direct methods in the calculus of variations

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